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Title: Cauchy’s theorem
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Series: Complex Analysis
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YouTube-Title: Complex Analysis 23 | Cauchy’s theorem
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Bright video: https://youtu.be/2yqtl0Sm8f4
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Dark video: https://youtu.be/2-u3cT_JysU
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Ad-free video: Watch Vimeo video
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Forum: Ask a question in Mattermost
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Quiz: Test your knowledge
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Dark-PDF: Download PDF version of the dark video
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Print-PDF: Download printable PDF version
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Thumbnail (bright): Download PNG
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Thumbnail (dark): Download PNG
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Subtitle on GitHub: ca23_sub_eng.srt missing
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Download bright video: Link on Vimeo
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Download dark video: Link on Vimeo
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Timestamps (n/a)
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Subtitle in English (n/a)
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Quiz Content
Q1: Let $f : D \rightarrow \mathbb{C}$ be a holomorphic function and $\gamma$ be a curve in $D$ where the image is a polygon. Which statement is correct?
A1: One needs more information.
A2: $$ \oint_{\gamma} f(z) , dz = 0 $$
A3: $$ \oint_{\gamma} f(z) , dz \neq 0 $$
A4: $$ \oint_{\gamma} f(z) , dz = 1 $$
Q2: Let $f : \mathbb{C} \rightarrow \mathbb{C}$ be given by $f(z) = \cos(z)$ and $\gamma$ be a closed curve in $D$. Which statement is correct?
A1: $$ \oint_{\gamma} f(z) , dz = 0 $$
A2: One needs more information.
A3: $$ \oint_{\gamma} f(z) , dz \neq 0 $$
A4: $$ \oint_{\gamma} f(z) , dz = 1 $$
A5: $$ \oint_{\gamma} f(z) , dz = 2 \pi i $$
Q3: Let $D = B_{1}(2i)$ and $f : D \rightarrow \mathbb{C}$ be given by $f(z) = \frac{1}{z}$. In addition, let $\gamma$ be a closed curve in $D$. Which statement is correct?
A1: One needs more information.
A2: $$ \oint_{\gamma} f(z) , dz = 0 $$
A3: $$ \oint_{\gamma} f(z) , dz \neq 0 $$
A4: $$ \oint_{\gamma} f(z) , dz = 1 $$
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Last update: 2024-10
